The Englishman, 42, has been Carlo Ancelotti's right-hand man since he was at Chelsea, and followed him to the Bernabeu - culminating in helping Real win their 10th European cup on Saturday night.
Clement was an academy coach at Chelsea and Fulham in the 90s, before taking over the Republic of Ireland's Under-21s.
He went on to become a coach of Chelsea's senior side alongside Ancelotti, before assistant roles at Blackburn, PSG (also under Ancelotti) and Real.
"I think the time for me to be a number one is soon," he said.
"A few opportunities have come my way, but this (Real Madrid) is a difficult place to leave.
"It's a great club, a great city, a great tradition and it gives you the opportunity to win things.
"I'm not ruling anything out. It's more than likely it will be in England, but if a nice opportunity came up in another country I wouldn't rule it out."
"Carlo has given me a lot of confidence and given me the belief that one day I can do it," Clement said.
"But he hasn't kicked me out of the door just yet."
